18 August 09Mark Rayner – Momentum measurement by The TOFs1 Momentum measurement by the TOFs A correction to an O(4 MeV/c) bias on the current muon momentum measurement which can be independently applied to individual muons

18 August 09Mark Rayner – Momentum measurement by The TOFs2 Momentum measurement by the TOFs Muon energy approximately constant between TOFs –p/E = s/t s = path length between TOF0 and TOF1 (~8m) t = time of flight (~29ns at 250 MeV/c) Predicted resolution –4.7 MeV/c at 250 MeV/c Bias on the measurement –Time of flight mis-calibration by 10 ps: 0.57 MeV/c bias –Path length over/underestimation by 10 mm: 2.1 MeV/c bias

18 August 09Mark Rayner – Momentum measurement by The TOFs3 Monte Carlo simulation Marco’s  =6mm p absorber =200 MeV/c centre of the e-p matrix beam –Mean Pz = 270 MeV/c at TOF0 (see left histogram) P/E=s/t where s=true path length –Measures true p before TOF1 with RMS error 0.65 MeV/c –See right histogram –Width and bias due to dE/dx in the air between TOF0 and TOF1

18 August 09Mark Rayner – Momentum measurement by The TOFs4 Should we simply approximate s=  z? P/E=  z/t –RMS error 3.38 MeV/c –Bias MeV/c –Due to the width of the  =s-  z distribution

18 August 09Mark Rayner – Momentum measurement by The TOFs5 Monte Carlo: Full demonstration of P reconstruction Iterative calculation of increasingly good s=  z+  and P –Begin with P from P/E=  z/t 1)Calculate a linear transfer map at P from TOF0 to TOF1 (top hat quadrupoles) 2)Deduce x 0 ’ and y 0 ’ from x 1 and y 1 3)Integrate ds while tracking the initial trace space vector through the beam line 4)Make a better estimate of P from P/E=s/t 5)Make a small Bethe-Bloch correction for the energy loss in air between the TOFs

18 August 09Mark Rayner – Momentum measurement by The TOFs6 Result of the full Monte Carlo

18 August 09Mark Rayner – Momentum measurement by The TOFs7 Conclusion This method eliminates path length bias It is implemented as a G4MICE application –It should replace the current p/E=  z/t automatic momentum reconstruction –Emittance measurement is a natural by-product at minimal extra cost –An online monitoring GUI can be produced to plot p and  in real time It initially requires –Quadrupole currents I 7, I 8 and I 9 –Quadrupole and TOF positions z 0, z 7, z 8, z 9, z 1 –From database? For individual muon P measurements it requires –t, x 0, y 0, x 1, y 1, PID This method will not work with positrons –Therefore TOF calibration must use simulation of positron beam